Question

Which ordered pair is a solution to this equation?

Answer 1

1. 2x + 3y = 16....just a matter of subbing...answer is (5,2) <=

2. to find the x int, sub in 0 for y and solve for x
    -2x + 5(0) = -20
     x = -20/-2
    x = 10......or (10,0) <=

3. (2,-5)(4,1)...using slope formula : (y2 - y1) / (x2 - x1)
    slope = (1 - (-5) / (4 - 2) = 6/2 = 3 <=
    
4. y = 4x - 3....the first 3 are true

Answer 2

Part 1) Which ordered pair is a solution to this equation?

$2x + 3y = 16$

Substitute the values of each pair ordered in the equation to find the solution

A. $(5, 2)$

$2*5 + 3*2 = 10+6\\ 16=16$

The pair ordered A is a solution

B. $(3, 2)$

$2*3 + 3*2 = 6+6$

$12\neq 16$

The pair ordered B is not a solution

C. $(11, 1)$

$2*11 + 3*1 = 22+3$

$25\neq 16$

The pair ordered C is not a solution

D. $(7, 2)$

$2*7 + 3*2 = 14+6$

$20\neq 16$

The pair ordered D is not a solution

therefore

the answer part 1) is

The ordered pair A. $(5, 2)$ is a solution of the equation

Part 2) The equation of a line is $-2x+5y=-20$

we know that

the x-intercept is when the value of y is equal to zero

so

for $y=0$

Find the value of x

substitute

$-2*x+5*0=-20$

$-2*x=-20$

$x=10$

therefore

the answer part 2) is

The x-intercept is equal to $10$

Part 3) What is the slope of the line passing through the points $(2, -5)$ and $(4, 1)$?

we know that

the slope of the line is equal to

$m=\frac{(y2-y1)}{(x2-x1)}$

Substitute the values in the formula

$m=\frac{(1+5)}{(4-2)}$

$m=\frac{(6)}{(2)}$

$m=3$

therefore

the answer part 3) is

The slope of the line is equal to $3$

Part 4) Select all statements that are true about the linear equation.

$y = 4x- 3$

Statements

a) The graph of the equation is the set of all points that are solutions to the equation

This statements is True------> Any point that belongs to the graph of the equation is the solution to the equation

b) The point $(0,-3)$ is on the graph of the equation

substitute the values in the equation

$-3 = 4*0- 3$

$-3 = - 3$ ----> the point is on the graph of the equation

therefore

This statements is True

c) The point (1, 1) is on the graph of the equation

substitute the values in the equation

$1 = 4*1- 3$

$1 = 1$ ----> the point is on the graph of the equation

therefore

This statements is True

d) The graph of the equation is a single point representing one solution to the equation

This statements is False ------> the equation graph are infinite points, representing infinite equation solutions